AI 中文总结
研究固定闭三维流形中无完美适配的伪阿诺索夫流，通过证明其有限性，进而推断出固定三维流形中转向三角剖分的有限性。
AI 中文摘要
我们证明了一个固定的闭三维流形至多允许有限多个无完美适配的伪阿诺索夫流，并由此推断出固定三维流形中转向三角剖分的有限性。
英文摘要
We show that a finite volume cusped hyperbolic 3-manifold admits at most finitely many veering triangulations, and in fact this number is bounded above by the number of Giroux torsion free tight contact structures. This resolves Kirby problem K3 3.21e. More generally, for any 3-manifold $M$ and any link $L$, we show finiteness for the family of pseudo-Anosov flows which admits a \emph{strictly positive Birkhoff section relative to $L$}. Combined with work of Li, this implies that a fixed closed $3$-manifold admits at most finitely many pseudo-Anosov flows without perfect fits. This resolves Kirby problem K3 3.21d.
Commentsv2: rewrote the introduction and some of the text to make the main theorem appear in full generality
